**Punjabi University Patiala MCA Entrance Exam Syllabus**

**English (Objective) :**This paper will have questions from English Grammar such as choosing correct spellings, completion of sentences with suitable prepositions/articles, meaning of a word, synonym, antonym, meaning of idioms and phrases, choosing/ correcting grammatical errors in a part of given sentence, filling the blanks with correct form of verb, adjectives, adverbs etc. (Essay writing, Précis witting, unseen passage, for comprehension etc.)**Mathematics****UNIT-I****NUMBER SYSTEM**

- Statements of the algebraic and order properties of the system of natural numbers, integers, rational numbers and real numbers and simple basic deductions from these properties.
- The statements of the following results with illustrations but without proofs:

- Rational numbers as terminating decimals or as non-terminating recurring decimals, inadequacy of rationals.
- Irrational numbers as non-terminating, non-recurring decimals.

- Representation of real numbers as points on a line, absolute value of real numbers.

- Complex numbers, representation of complex numbers, real and imaginary parts, modulus and argument of a complex number, conjugate of a complex number.
- Statements of the principle of mathematical induction in respect of natural number and simple application.
**TRIGONOMETRY**

- Angles and their measure in degrees and radians. Trigonometric function of angles of arbitrary magnitudes.
- Addition formulae, sine, cosine and tangent of multiples and submultiples of angles. Periodicity and graph of sine, cosine and tangent functions.
- Trigonometrical ratio of related angles.
- Solution of simple trigonometric equations.
- Sine and cosine formulae for triangles and simple cases of solution of triangles, problems on heights and distances.

**COORDINATE GEOMETRY**

- Distance formula and section formula.
- Equation of line in a plane, general equation, equation of first degree, angle between two lines, parallel and perpendicular lines, distance of point from a line, family of lines.
- Equation of a circle, general equation, equation of tangent and normal to a circle, radical axis of two circles.
- Parametric representations of a circle.
- Conic sections, equations of parabola, ellipse and hyperbola in standard form.

**COORDINATE GEOMETRY IN SPACE**

- Cartesian equations of lines and planes in three dimensions, angle between two lines, between a line and a plane and also between two planes, distance of a point from a plane, shortest distance between two lines, equations of any plane passing through the intersection of two planes.
- Equation of a sphere, general equation.

**UNIT-II****FUNCTIONS**

- Examples of real functions and their graphs.
- Algebra of real functions, ex. of polynomial & rational functions.
- One-one, on to and inverse functions.

**QUADRATIC EQUATIONS AND INEQUATIONS**

- Quadratic equations and their solutions, relationship between the roots and coefficients, formation of quadratic equations with given root, criteria for the nature of the roots of a quadratic equations.
- Solution of quadratic in equations with their graphical representation.

**SEQUENCES AND SERIES**

- AP, GP and their sums.

**PERMUTATIONS, COMBINATIONS & THE BINOMIAL THEOREM**

- Elementary study of combinations, value of P and C, simple applications.
- Binomial theorem for a positive integral index and its proof.
- Statement of the binomial theorem for an arbitrary index & its application to approximations.

**UNIT-III****MATRICES & DETERMINANTS**

- Determinants of square matrices of order not exceeding 3 and application to solutions of linear equations having a single solution. Cramer’s rule.
- Sum and differences of matrices with not more than 3 rows & 3 columns.
- Geometrical transformations (reflection, rotation, translation and enlargement) in a plane and their representation matrices, composite of reflections in two parallel lines and two intersecting lines.
- Composition of transformations and products of matrices, non- commutativity of matrix multiplication, examples of non-zero matrices such that their product is zero matrix.
- Non-singular matrices and their inverses, adjoint of a matrix.
- Consistency of systems of two or three linear equations with two or three unknowns, linear equations in matrix notations, applications of matrices in solving simultaneous equations in three variables.

**CALCULUS**

- Notions of right handed and left handed limit and the limit and continuity of a function introduced through examples and illustrated graphically as well as numerically. Properties of continuous functions, continuity of polynomial, trigonometric, exponential and logarithmic functions.
- Derivative of a function at a point, Derivative as instantaneous rate of change and slope of a curve. Tangents and normals.
- Derivative of polynomial function.
- Interpretation of the sign of the derivative at a point.

**UNIT-IV****CALCULUS**

- Derivatives of quotients of functions and of rational functions.
- Rolle’s Theorem illustrated geometrically, Derivations of the Lagrange’s Mean Value Theorem and its geometrical interpretation, Relation between the sign of derivative in an integral and monotonicity.
- Determination of maximum and minimum values of a function. Graphs of polynomial functions of degree not exceeding 4.
- Graphs and derivatives of trigonometric, inverse trigonometrical, exponential and logarithmic functions. Differentiation of implicit function, logarithmic differentiation, derivatives of functions expressed in parametric forms, derivative of higher order.
- Primitives of functions and their calculations in simple cases.
- Integration by substitution and by parts.
- The definition of definite integral as the limit of a sum motivated by the determination of areas. Evaluation of definite integrals, properties of definite integrals.
- Applications to determination of area under curves in simple differential cases. Differential Equations, order and degree, formation of a differential equation, general and particular solution of a differential equation, solution of a differential equation by the method of separable variables. Homogenous equation and their solution: Solution of the linear equation of the first order with constant coefficients.

**UNIT-V****VECTORS**

- Vectors as a directed line segment, Addition of vectors, Multiplication of a vector by real number.
- Position vector of a point. Section Formula.
- Application of vectors of some geometrical results.
- Scalar and vector product of two vector.
- Scalar triple product, vector triple product.

**STATISTICS**

- Population and sample.
- Measures of central tendency and dispersion.
- Point and interval estimation (of mean only).
- Scatter diagrams and Pearson’s correlation coefficient.
- Calculation of the regression coefficient and the two lines of regression by the methods of least squares.

**PROBABILITY**

- Random experiments and sample space, events.
- Probability on a discrete sample space, addition theorem.
- Conditional probability, multiplication theorem
- Independent events
- Random variables (mean and variance. Calculations for simple probability distributions).
- Normal distribution.

**Mental Ability :**This paper will have the topics of logical reasoning, graphical analysis, analytical reasoning, and quantitative comparisons and series formation.

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